Theorems · Theorem · linear algebra
Module.End.pos_finrank_genEigenspace_of_hasEigenvalue
∀ {K : Type v} {V : Type w} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] [FiniteDimensional K V]
{f : Module.End K V} {k : ℕ} {μ : K}, f.HasEigenvalue μ → 0 < k → 0 < Module.finrank K ↥((f.genEigenspace μ) ↑k)The generalized eigenspace of an eigenvalue has positive dimension for positive exponents.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Fieldstatement and proof · cited by 7,404
- Submodulestatement · cited by 7,192
- ENatstatement · cited by 4,985
- zero_addproof · cited by 2,366
- FiniteDimensionalstatement and proof · cited by 1,854
- Module.finrankstatement · cited by 1,770
- OrderHomstatement · cited by 934
- Module.Endstatement and proof · cited by 774
- Module.End.genEigenspacestatement and proof · cited by 70
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.iSup_maxGenEigenspace_eq_topproof · cited by 1